The Mathematics of Computerized TomographyWiley, 03.10.1986 - 222 Seiten The central subject of this book is the reconstruction of a function from line or plane integrals, with special emphasis on applications in science, radiology and engineering. It not only covers the relevant mathematical theory of the Radon transform and related transforms, but also studies more practical questions such as sampling, resolution, stability and accuracy. Much of the book is devoted to the derivation, analysis and practical examination of reconstruction algorithms, both for standard problems and problems with incomplete data. |
Inhalt
The Radon Transform and Related Transforms | 9 |
Sampling and Resolution | 54 |
Illposedness and Accuracy | 85 |
Urheberrecht | |
5 weitere Abschnitte werden nicht angezeigt.
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
a₁ Abramowitz and Stegun apply approximation artefacts assume band-limited functions C₁ compute constant converges convolution defined derivatives discrete Fourier transform eigenvalues error essentially b-band-limited estimate exterior problem fan-beam filtered backprojection algorithm finite follows Fourier reconstruction function f Gegenbauer polynomials harmonics of degree hence ill-posed problems incomplete data problems inner integral interpolation inversion formula iteration Kaczmarz's method L₂ Lemma Let fe limited angle line integrals linear matrix norm obtain operator orthogonal projection parallel geometry plane polynomial of degree Proof Radon transform range sampling scanning geometry Section singular value decomposition Sobolev spaces solution solve spherical harmonics step Theorem 1.1 Theorem II.1.1 Toeplitz matrix transform of length Tuy's uniquely vanishes zero Σ Σ